Problem: Simplify the following expression: $ x = \dfrac{-5}{8} - \dfrac{n + 10}{3n + 10} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3n + 10}{3n + 10}$ $ \dfrac{-5}{8} \times \dfrac{3n + 10}{3n + 10} = \dfrac{-15n - 50}{24n + 80} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{n + 10}{3n + 10} \times \dfrac{8}{8} = \dfrac{8n + 80}{24n + 80} $ Therefore $ x = \dfrac{-15n - 50}{24n + 80} - \dfrac{8n + 80}{24n + 80} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{-15n - 50 - (8n + 80) }{24n + 80} $ Distribute the negative sign: $x = \dfrac{-15n - 50 - 8n - 80}{24n + 80}$ $x = \dfrac{-23n - 130}{24n + 80}$